SP#7: Unit Q Concept 2-Finding trig functions using identities

This post was made in collaboration with Jorge Molina. Please visit the other awesome posts on his blog by going here.

Hello there fellow students. Before starting the problem there are a few things you must be aware about. First of all, make sure not to solve this problem straight using trigonometry. We will be using identities for this problem, including: reciprocal identities, ratio identities, and Pythagorean identities. Secondly, solving identities are much easier than we think of them to be. Make sure to look at the clues to help you solve for the problem. Lastly, make sure when rationalizing to be careful what you are multiplying and always look for simplification. Other than that, relax, enjoy and solve your life away!

Photo-credits to the fab-u-lous Victoria Ventura

Photo-credits to the fab-u-lous Victoria Ventura

Photo-credits to the fab-u-lous Victoria Ventura

Photo-credits to the fab-u-lous Jorge Molina

Photo-credits to the fab-u-lous Jorge Molina

Photo-credits to the fab-u-lous Jorge Molina

Photo-credits to the fab-u-lous Victoria Ventura

SP#6: Unit K Concept 10-Infinite Geometric Series

In order to solve this problem, a big help would be knowing the infinite geometric series equation. As explained in the picture to solve your a sub 1 and ratio is pretty simple. You can refer back to earlier concepts. To find a sub 1, it would just be the first term in the series. To find the ratio you must divide the second term by the first term. Although the whole number is left out throughout the problem, remember to add it in at the end and only then well you have your answer to the problem.

SP#5: Unit J Concept 6

What do you need to know in order to understand this problem and concept?

In order to understand this concept alone, you must remember that unlike concept five in which it has distinct factors this concept does not. This is at a difficult level and does apply matrices. Make sure to be patient and be clear on your work, in order to track a mistake, if done. Other than that, have fun and enjoy Student Problem#5.

SP#4: Unit J Concept 5

What do you need to know in order to understand this problem and concept?

In order to understand this problem you must understand that this concept has distinct factors. This concept consists of decomposition. And although matrices might seem way behind us, we will have to apply it in this problem.  Luckily for us, we can use our graphing calculator. The main tool you must use is, the tool from algebra, to add fractions and you will be set for life. Well not really, just for these two concepts. Good luck and enjoy.

SP#3-Graphing exponential functions

What does the viewer need to pay special attention to in order to understand?

First of all to understand how to graph the equation and where the boundary is, its the asymptote which is y=h. For this equation it would be y=-2. Secondly, because the equation is negative and the boundary is at -2, that means no x-intercepts because when solving for the x-intercept, a log of a negative number cannot be solved, it is undefined. Lastly, to find your y-intercept you must plug in zero and from there solve for the rest. 

SP#2: Unit E Concept 7-Graphing a polynomial and identifying all key parts

1. What is the problem?

This problem presents us how to use extremas, intercepts, end behavior, mulitiplicities and factoring, all into one bunch. The extremas let us know when are the maximum and minimum points on the graph. The intercepts let us know where on the graph do we cross the x and y axis. End Behavior lets us know how the graph will look, the multiplicities will lets us know how the graph in between will look like.

2.What do you need to pay special attention to?

While figuring out the problem you must pay special attention to the factoring, if the equation is not factored correctly, things will get messy. second, pay attention to your end behavior and whether its right or not. Lastly, pay attention when drawing your graph whetger on a point does it bounce off, go through, or curve?

SP#1: Unit E Concept 1-Graphing a quadratic and identifying all key parts

This problem is a quadratic problem. The point of this problem is to be able use all the parts of the quadratic to find many different useful parts to draw out a graph of that equation. The parts that need to be found are: the parent function equation, vertex, y-intercept, x-intercepts, and the axis.

In order to understand the equation, you must right out your steps clearly. Important parts of the equation or the x-intercepts. If those turn out to be x-intercepts with square roots, you must simplify as much possible. And once in putting the x-intercepts into the calculator to round the nearest tenth for the exact and approximate x-intercepts.